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Chapter 17: Problem 4

Define entropy. What are the units of entropy?

Short Answer

Expert verified
Entropy is a measure of the number of specific ways a system may be arranged, often assumed to be a measure of disorder. The unit for measurement is joule per kelvin (J/K) or commonly reported in calories per degree Celsius.

Step by step solution

01

Define Entropy

Entropy is a measure of the number of specific ways in which a system may be arranged, often taken to be a measure of disorder, or a measure of progressing towards thermodynamic equilibrium. It is a state function that is often erroneously referred to as the 'measure of disorder', with disorder being more accurately described by the number of microscopic configurations corresponding to a thermodynamic system in a state specified by a macrostate.
02

Units of Entropy

The SI unit for entropy is joule per kelvin (J/K). However, it is commonly reported with the units of calories per degree Celsius for many processes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamic Equilibrium
The concept of thermodynamic equilibrium is crucial to understanding many aspects of thermodynamics, including entropy. A system is said to be in thermodynamic equilibrium when it is in mechanical, thermal, and chemical equilibrium all at once. This means that:
  • The forces within the system are balanced, so it is in mechanical equilibrium.
  • The temperature is uniform throughout the system, indicating thermal equilibrium.
  • The chemical potential is consistent throughout, signifying chemical equilibrium.
When all these conditions are met, there is no net flow of energy or matter, and hence, the system is in its most stable state. The concept of entropy is intimately linked with thermodynamic equilibrium as systems naturally progress toward this state, where entropy is maximized.
State Function
A state function is a property whose value does not depend on the path taken to reach that specific value, only on the current state of the system. Entropy is an excellent example of a state function. This is in contrast to path functions, like heat or work, which depend on the specific transitions between states. State functions are significant because they allow us to simplify the analysis of thermodynamic systems. Whether a system has gained or lost heat can affect its entropy, but the change ultimately relies on the differences in the initial and final states, not on how that change was achieved. Hence, state functions provide a clear, snapshot-like view of the system's properties at any point.
SI Unit
In the field of science, understanding the SI unit of a measure is fundamental. For entropy, the SI unit is joules per kelvin (J/K). This unit effectively communicates the amount of energy dispersed or spread out at a specific temperature. The use of J/K as the SI unit for entropy aligns with its definition, which involves energy distribution in relation to temperature. However, in various domains such as chemistry, entropy is occasionally expressed in calories per degree Celsius. While less common in this era of global standardization, this can still be encountered, especially in older literature or specialized contexts.

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Most popular questions from this chapter

Give a detailed example of each of the following, with an explanation: (a) a thermodynamically spontaneous process; (b) a process that would violate the first law of thermodynamics; (c) a process that would violate the second law of thermodynamics; (d) an irreversible process; (e) an equilibrium process.

Entropy has sometimes been described as "time's arrow" because it is the property that determines the forward direction of time. Explain.

Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(\left.K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) and \(\mathrm{CH}_{2} \mathrm{ClCOOH}\) (chloroacetic acid, \(K_{\mathrm{a}}=1.4 \times 10^{-3}\) ). (a) Calculate \(\Delta G^{\circ}\) for the ionization of these acids at \(25^{\circ} \mathrm{C}\). (b) From the equation \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ},\) we see that the contributions to the \(\Delta G^{\circ}\) term are an enthalpy term \(\left(\Delta H^{\circ}\right)\) and a temperature times entropy term \(\left(T \Delta S^{\circ}\right) .\) These contributions are listed below for the two acids: $$ \begin{array}{lcc} \hline & \Delta H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & T \Delta S^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) \\ \hline \mathrm{CH}_{3} \mathrm{COOH} & -0.57 & -27.6 \\ \mathrm{CH}_{2} \mathrm{ClCOOH} & -4.7 & -21.1 \\ \hline \end{array} $$ Which is the dominant term in determining the value of \(\Delta G^{\circ}\) (and hence \(K_{\mathrm{a}}\) of the acid)? (c) What processes contribute to \(\Delta H^{\circ} ?\) (Consider the ionization of the acids as a Br酶nsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\)

For each pair of substances listed here, choose the one having the larger standard entropy value at \(25^{\circ} \mathrm{C}\). The same molar amount is used in the comparison. Explain the basis for your choice. (a) \(\mathrm{Li}(s)\) or \(\mathrm{Li}(l)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) or \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(l)\) (Hint: Which molecule can hydrogen-bond?); (c) \(\operatorname{Ar}(g)\) or \(\operatorname{Xe}(g) ;\) (d) \(\operatorname{CO}(g)\) or \(\mathrm{CO}_{2}(g)\) (e) \(\mathrm{O}_{2}(g)\) or \(\mathrm{O}_{3}(g) ;(\mathrm{f}) \mathrm{NO}_{2}(g)\) or \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\)

Why is it more convenient to predict the direction of a reaction in terms of \(\Delta G_{\text {sys }}\) instead of \(\Delta S_{\text {univ }}\) ? Under what conditions can \(\Delta G_{\text {sys }}\) be used to predict the spontaneity of a reaction?
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